I have a database that is being replicated to another, and I'm planning to create an index on one of the source database tables. Do I need to shutdown replication before doing that? and do I need to create the index in the destination database manually?
1) normal replication : you can create your index without stoping the replication. You can create in in the primary, replicated or both sides.
2) Warm standby replication : the creation of the index must be done on the primary. The RS will replicate the DDL too.